FoRTE baseline

Abstract

Forests in the US Upper Midwest have been a net C sink for a century, driven by their fast-growing, early successional species. However, the composition of these regrown forests has started to shift toward mid-successional species. Combined with changing climate and disturbance, this means that future biogeochemical and ecological dynamics in these forests are highly uncertain. Demographic vegetation models provide a tool for analyzing this uncertainty and its implications. Here, we evaluate the relative importance of model “structural” (which processes are represented, and how) and “parameter” (parameters used in those equations) uncertainty, asking: (1) Which processes are most important to accurately model community succession and C cycling in Upper Midwest forests? (2) What are the relative contributions of parameter vs. structural uncertainty? We ran ensembles of the Ecosystem Demography model v2.2 (sampling over parameter uncertainty) from 1900 to 2000 with different representations of key processes important to competition for light. We then compared the magnitude of structural (across representations) and parameter (within each representation) uncertainty, and assessed which submodel-parameter combinations reproduced observed C fluxes and succession. Our simulations agreed well with observed net primary productivity but systematically underestimated leaf area index. Overall, parameter uncertainty contributed more than structural uncertainty to total simulation uncertainty, but the amount of parameter uncertainty varied with model structure. We conclude that: (1) targeted data collection to constrain vegetation model parameters should be a higher priority than model development; (2) parameter sensitivity analyses are not necessarily generalizable across model structures; and (3) robust model validation requires scrutiny of multiple different variables, including those related to vegetation productivity, structure, and composition.

Introduction

Forests are a defining feature of the US North. This region is the most heavily forested region in the US, and these forests are an essential provider of employment and recreation opportunities and other ecosystem services for the region’s people, and of habitat for the region’s wildlife (Shividenko et al. 2005, Shifley et al. 2012). In addition, the forests of the Upper Midwest in particular have been a net carbon sink for most of the past century, as fast-growing early successional species established and thrived following near-complete deforestation around the end of the 19th Century (Birdsey et al. 2006, Williams et al. 2012). However, the fate of these forests is highly uncertain. For one, many Upper Midwest forests are undergoing a shift in community composition from early-successional to mid-successional species, and the ecological and biogeochemical consequences of this transition are not well-established (Gough et al. 2016). In addition, these forests face a multitude of direct and indirect pressures from both biotic and abiotic sources (Shifley and Moser 2016), including longer and more severe droughts (Gustafson et al. 2016, Liénard et al. 2016, Swanston et al. 2017), non-native insects and pathogens (Lovett et al. 2016), and more. Collectively, these processes have culminated in forests that are different from their pre-settlement climax counterparts (Wolter and White 2002, Stearns and Likens 2002, Thompson et al. 2013), and our ability to make predictions about such non-analog environments based on the past is limited.

More reliable predictions can in theory be obtained by using dynamic vegetation models that explicitly represent processes involved in forest growth and mortality. Vegetation models fall broadly along the following spectrum of complexity, which is a direct consequence of trade-offs between realism and process fidelity on one hand and tractability, computational demand, and data requirements on the other (Hawkes 2000). On one side are relatively simple “big leaf” models—such as PNET, SiBCASA, and Biome-BGC—in which the vegetation at a particular location consists essentially of a single large “plant” whose characteristics are the (weighted) average of all the vegetation at that site. A common application of these models was simulating the land surface boundary condition for atmospheric general circulation models, though similar models have been (and continue to be) applied successfully to simulate biogeochemical processes in many ecosystem science contexts. On the other end of the spectrum are “individual-based” models (a.k.a. “gap models”), which explicitly simulate multiple indivduals competing for resources at a single site (Shugart et al. 2015). Examples of such models are LANDIS (Mladenoff 2004, Scheller et al. 2007) and UVAFME. Because these models can explicitly represent inter-specific differences in plant productivity, resource allocation, and stress tolerance (among others), as well as the competition that emerges out of these differences, they may be better able to represent changes in ecosystem-scale processes, especially in no-analog conditions (Purves and Pacala 2008). Between these two extremes are models that use approximations attempt to capture the emergent biogeochemical and ecological outcomes of interactions between individual plants without the need for explicitly simulating each individual (Purves and Pacala 2008). One specific example of this approach is the Ecosystem Demography model (ED2; Moorcroft et al. 2001, Medvigy and Moorcroft 2011, Longo et al. 2019b), which is the focus of this study.

Regardless of vegetation model complexity, their projections are inherently uncertain. This uncertainty comes from many different sources, which can broadly be classified into the following categories: Driver uncertainty refers to uncertainty in data about processes not represented by the model (e.g. weather and climate for vegetation models). Initial condition uncertainty arises from the fact that models have to start somewhere, and the exact conditions at the place and time simulations begin are frequently unknown. Process or structural uncertainty arises because vegetation models necessarily only represent a subset of all processes involved in plant biology, and that the process that are included can usually be represented in multiple different ways (i.e. which processes are included, and how they are represented). Finally, parameter uncertainty arises because of natural variability and imperfect calibration of the above process representations. The relative importance of these sources of uncertainty in ecological forecasts is a key question because it is directly related to future research priorities. For example, in the atmospheric science community, the insight that meteorological forecasts were most sensitive to initial condition uncertainty (Lorenz REF) led to a multi-decadal research agenda aimed at constraining the initial state with improved observations, which has directly contributed to a steady and persistent improvement in meteorological forecasts over the last several decades.

Many ecosystem modeling studies have looked at these categories of uncertainty independently. Perhaps the most work has been done on parameter uncertainty in ecosystem models. Dietze et al. (2014) investigated which parameters were most important to ED2 predictions of C sequestration across a diverse range of sites in North America. The found that the parameters contributing the most to overall predictive uncertainty were those related to growth respiration, mortality, stomatal conductance, and water uptake, and that parameter uncertainty varied with biome. More recently, Raczka et al. (2018) evaluated parameter uncertainty over 100 year time scale at the Willow Creek Ameriflux site, and found that the most important parameters to model uncertainty were quantum efficiency of photosynthesis, leaf respiration, and soil-plant water transfer. Another recent study assessed parameter uncertainty in ED2 as part of its overall goal of parameterizing the model for sagebrush (Pandit et al. 2018). They found that the most important parameters were specific leaf area, the maximum rate of carbon fixation (V_cmax), slope of stomatal conductance, the fine-root to leaf carbon ratio, and the fine root turnover rate. Another study looked specifically at contributions to uncertainty from parameters related to canopy radiative transfer, and found that parameters related to both canopy structure and leaf optical properties had a large impact on predictions of net primary productivity (Viskari et al. 2019). {Driver uncertainty – a few examples?} Other studies have investigated structural uncertainty.. Numerous vegetation model intercomparison studies have demonstrated that different models produce significantly different projections of overall land carbon sequestration (Friedlingstein et al. 2006, 2014), response to CO₂ fertilization (Zaehle et al. 2014, Walker et al. 2015, Medlyn et al. 2015), and soil C sequestration (Sulman et al. 2018), among others. In particular, Lovenduski and Bonan (2017) found that model structural uncertainty was the primary source of uncertainty in Earth system model projections of the land C sink. This structural uncertainty has been attributed to differences in model representations of key processes, including canopy radiative transfer (Fisher et al. 2017), soil biogeochemistry (Wieder et al. 2017, Sulman et al. 2018), stomatal conductance (Franks et al. 2018), and photosynthesis (Rogers et al. 2016). However, the extent to which specific processes contribute to model uncertainty is difficult to evaluate from model intercomparisons because different models are different from each other in too many different ways, meaning that structural effects are confounded with other uncertainty sources. Moreover, comparative analysis of contributions of different types of uncertainty to model projections are rare in the ecosystem modeling literature.

This study focuses on the interaction between parametric and structural uncertainty in the ED2 model. Our study is organized around the following guiding questions: (1) Which processes related to light utilization are most important to accurately modeling community succession and C cycle dynamics in temperate forests of the Upper Midwest? (2) What is the cost of considering these processes, in terms of additional parameteric uncertainty? (3) What are the relative contributions of parameteric uncertainty (data limitation) vs. structural uncertainty (theoretical limitation?)? To answer these questions, we ran ED2 ensemble simulationes with a factorial combination of submodels related to radiative transfer formulation (two-stream vs. multiple scatter), horizontal competition (finite canopy radius vs. complete shading), and trait plasticity (whether or not SLA and Vcmax vary with light level) We then used sensitivity and variance decomposition analyses to evaluate the contribution of parameter uncertainty for each model configuration, exploring the ecological implications of the results.

Methods

Site description

We performed this study at the University of Michigan Biological Station (UMBS; Ameriflux site US-UMd, 45.5625\(^{\circ}\), -84.6975\(^{\circ}\)), located in Northern Lower Michigan, USA. The area surrounding the research station is 87% well-drained upland forest and 13% wetland (Bergen and Dronova 2007); the focus of this study is on the former. The landscape geography of the UMBS upland forest is 20.4% moraine, 37.8% high outwash plain, 31.3% low outwash plain, 5.7% lake-margin terrace, 3.6% ice-contact, and 1.2% lowland glacial lake (Bergen and Dronova 2007). Most of the UMBS upland forest canopy is dominated by temperate deciduous early-successional species, most importantly Populus grandidentata (bigtooth aspen) and, to a lesser extent, Betula papyrifera (paper birch), with Acer saccharum (sugar maple), Acer rubrum (red maple), Fagus grandifolia (American beech), Tilia americana (basswood), Betula alleghaniensis (yellow birch), Fraxinus americana (white ash), Tsuga canadensis (eastern hemlock), Quercus rubra (northern red oak), Pinus strobus (white pine), and Pinus resinosa (red pine) existing in various fractions in the understory (and, in patches, in the canopy). This composition is a legacy of the site’s disturbance history: The site was intensively logged in the late 1800s and early 1900s, and experienced regularly recurring fires until the mid-1920s, at which point a regime of active fire suppression started that has persisted to the present day. As a result, the average stand age in 2013 was 95 years. The majority of the forest that is aspen-dominated is undergoing succession to “northern hardwood” (maple, beech, basswood, birch, ash, hemlock), “upland conifer” (red and white pine), or “northern red-oak” ecotypes (Bergen and Dronova 2007).

Forest stands at UMBS were previously exposed to experimental disturbance as part of the Forest Accelerated Succession Experiment (FASET). BBL: what’s the canonical FoRTE citation? Hmm. http://dx.doi.org/10.1111/nph.15227

Ecosystem Demography Model (version 2.2)

For this study, we used the Ecosystem Demography Model, version 2.2 (ED2). Below, we provide only a high-level description of key model features and focus in detail only on submodels and configurations specific to this study. A full description of the default configuration of the model is provided by Longo et al. (2019b).

The key feature of the “ecosystem demography” approach underlying the ED2 model is a system of partial differential equations that simulate the emergent mean behavior of “cohorts” of individuals of similar composition, size, and age (Moorcroft et al. 2001). The original “Ecosystem Demography” (ED) model (Moorcroft et al. 2001) was enhanced by Medvigy et al. (2009) (as ED2) with fully-coupled leaf physiology, canopy radiative transfer, and micrometeorology, and each of these components have been further refined over the last decade (culminating in ED2.2; Longo et al. 2019b). Various versions of the ED model have been validated in boreal (Medvigy and Moorcroft 2011), temperate (Medvigy et al. 2009, Dietze et al. 2014, Raczka et al. 2018), and tropical biomes (Moorcroft et al. 2001, Longo et al. 2019a), and have been applied in:

• paleoecological studies (Rollinson et al. 2017);
• free-air CO₂ enrichment studies (De Kauwe et al. 2013, Miller et al. 2015);
• estimation of potential carbon stocks (Hurtt et al. 2004)
• vegetation-climate feedbacks {Swann, etc}

ED2 represents both spatial and temporal variability hierarchically. The largest spatial unit is the “polygon”, within which all elements share the same meteorological forcings. Polygons are divided into multiple “sites”, each site with its own set of abiotic characteristics such as soil texture and topography. Sites are divided into discrete “patches” according to time since last disturbance. Finally, each patch is composed of an arbitrary (and dynamic) number of “cohorts”, representing the mean behavior of groups of plant individuals of similar size and composition. Temporal variability in ED2 is similarly hierarchical. Thermodynamics, including energy, water, and eddy (e.g. CO₂) fluxes, are resolved on the order of seconds. Biophysics, including photosynthesis, respiration, and radiative transfer, and the evaluation of energy, water, and CO2 budgets, are resolved on the order of minutes. Phenology and plant carbon balance are evaluated daily. Cohort dynamics, including structural growth, mortality, and reproduction, are evaluated monthly. Finally, patch dynamics (e.g. annual disturbances) are evaluated annually. In this study, we consider only a single patch (and, therefore, a single site and polygon) starting from a “near bare ground” condition.

{Brief summary of thermodynamics?} {Brief summary of water cycle?} BBL: maybe in one sentence each, but otherwise no, send ’em to a citation.

ED2 represents the carbon flux for each cohort as the net sum of contributions from turbulent mixing, leaf photosynthesis and respiration, (fine) root respiration, growth and maintenance respiration, and heterotrophic respiration. In addition, each cohort also has a virtual carbon balance that links fast processes like photosynthesis and respiration to slow processes like allocation (to growth, storage, and reproduction) and mortality.

The official ED2 source code is available at https://github.com/EDmodel/ED2, and the exact version used in this study (which includes minor revisions to accommodate the requirements of this study) can be obtained https://github.com/ashiklom/ED2/tree/b048950971e91699b78fc566df133caf977fda32.

ED2 submodels

In this study, we ran a factorial combination of the following ED2 configurations: (1) two-stream vs. multiple-scatter canopy radiative transfer models; (2) infinite vs. finite crown area (a.k.a. complete vs. partial shading); and (3) static vs. light-plastic traits.

Both canopy radiative transfer models in ED2 resolve the full vertical radiation profile within a patch as a function of canopy structure (leaf and wood area indices, crown area, leaf angle distribution) and incident solar radiation. The two models differ in the mathematical approximations of the underlying differential radiative transfer equations.

• Two-stream model (ED default)
  • Same general approach as in CLM 4.5 (Oleson et al. 2013), but rather than solving for just two layers (sunlit and shaded), solve for each canopy layer.
  • Set up the two-stream equations for each layer as a linear system and solve the entire set of equations numerically
  • Similar to approaches used in other models: JULES (Mercado et al. 2007), ORCHIDEE-CAN (Naudts et al. 2015), CLM(SPA) (Bonan et al. 2014)
  • For details, see Supplements S9 and S10 in (Longo et al. 2019b).
• Multiple scatter model
  • Based on Zhao and Qualls (2005)

The crown area submodel in ED2 determines the nature of competition for light between cohorts. In the default configuration (“infinite crown area”, or “complete shading”), the leaf area of a cohort is distributed across the entire horizontal area of a patch. This means that taller cohorts always receive more incoming radiation than shorter cohorts, even when the height difference is small. Put another way, this means that there is no horizontal competition, only vertical. This has been shown to excessively suppress competition from sub-dominant individuals and result in unrealistically homogeneous canopies (Fisher et al. 2015). In the alternate configuration (“finite crown area”, or “partial shading”), canopies take up only a fraction of the available horizontal area, meaning that multiple cohorts of similar height can receive the same level of light. The horizontal area of crowns is determined by allometric equations from Dietze and Clark (2008).

The third submodel we evaluated was trait plasticity. In the default configuration, all cohorts of a given plant functional type will have the same parameters, regardless of environmental conditions. This ignores the globally-documented intraspecific trait variability as a function of light level (Niinemets 2010, Keenan and Niinemets 2016). In the alternate configuration, as light level decreases (trees become more shaded), specific leaf area increases and V_cmax decreases, following empirical relationships from the tropics (Lloyd et al. 2010).

These sub-models are summarized in Table 1.

Table 1: ED-2.2 submodel descriptions

Name	Description	Color
Crown model
closed (default)	Cohort crowns take up entire patch area. Competition for light based only on height.	Light
finite	Cohort crown area is proportional to DBH according to PFT-specific allometry.	Dark
Radiative transfer model
two-stream (default)	Two-stream approximation (Sellers 1985, Oleson et al. 2013)	Primary (red, blue)
multi-scatter	Multiple-scatter approximation, following (Zhao and Qualls 2005)	Secondary (green, orange)
Trait plasticity
static (default)	SLA and Vc,max are constant	Cool (blue, green)
plastic	SLA increases, and Vc,max decreases, with light level	Warm (red, orange)

ED2 parameters

The full list of parameters in ED2 is large, with over 100 parameters per plant functional type. A full sensitivity and uncertainty analysis across all of these parameters is outside the scope of this study. Instead, we selected a subset of parameters that were identified as important by previous ED2 sensitivity studies (Dietze et al. 2014, Raczka et al. 2018, Viskari et al. 2019).

Three parameters are related to leaf-level physiology: Following the enzyme-kinetic model of Farquhar et al. (1980), the rate of photosynthesis is the minimum of light-limited and enzyme-limited reactions. The former are controlled by the quantum efficiency parameter—maximum efficiency with which absorbed photosynthetically active radiation is converted to CO₂. The latter are controlled by V_cmax, the maximum rate of carbon fixation by Rubisco. The water demand of photosynthesis is controlled by the stomatal slope, the sensitivity of stomatal conductance of CO₂ as a function of CO₂ concentration and humidity at the leaf surface (Ball et al. 1987, Leuning 1995). Three more parameters correspond to the respiration rates of leaves, roots, and “growth maintenance”.

Two more parameters control carbon allocation: One is the ratio of fine root to leaf biomass (fineroot2leaf, or q), and another is the ratio of “storage” carbon allocated to reproduction (r_fract).

Three parameters control various aspects of adult tree mortality, namely the density-independent mortality rate (mort3), and the time scale (mort1) and critical carbon balance (mort2) of mortality from carbon starvation. An additional parameter controls seedling mortality. Specific leaf area (SLA) is used to convert leaf biomass to leaf area index, which in turn is used in a variety of calculations related to canopy radiative transfer and micrometeorology.

Two additional parameters describe canopy structure in ways critical to the canopy radiative transfer: Canopy clumping factor describes how evenly leaf area is distributed in horizontal space (1 being perfectly evenly; 0 being a “black hole” where all leaves are concentrated in a single point); and leaf orientation factor describes the average distribution of leaf angles (-1 being perfectly vertical, 1 being perfectly horizontal, and 0 being random). Four parameters control leaf optical properties, namely the fractions of light reflected or transmitted in visible and near-infrared wavelengths (leaf_(reflect|trans)_(vis|nir)). Three other parameters:

• Fraction of litter carbon that enters the labile (fast) soil carbon pool (f_labile)
• Minimum plant height for reproduction (minimum_height)
• Soil-plant water conductance, or “water availability factor” (water_conductance)
• C:N ratio in fine roots (c2n_fineroot) and leaves (c2n_leaf)
• Leaf turnover rate (evergreen-only; leaf_turnover_rate)
• Proportion of dispersal that is “global” (nonlocal_dispersal)

The full list of parameters is shown in Table 2.

Table 2: Parameter descriptions. For additional information, see the ED2 model wiki.

ED Name	Description	unit_markdown	Raczka	Dietze
c2n_fineroot	C:N ratio in fine roots	unitless (mass ratio)	NA	NA
c2n_leaf	C:N ratio in leaves	unitless (mass ratio)	NA	NA
clumping_factor	Canopy clumping factor	NA	NA	NA
f_labile	Fraction of litter that goes to labile (fast) C pool	unitless (0-1)	Labile carbon	NA
fineroot2leaf (q)	Ratio of fine root to leaf biomass	unitless (mass ratio)	Root/Leaf carbon	Leaf:Root
growth_resp_factor	Fraction of daily C gain lost to growth respiration	unitless (0-1)	Growth respiration	Growth Resp
leaf_reflect_nir	Leaf reflectance in NIR range (700-2500 nm)	unitless (0-1)	NA	NA
leaf_reflect_vis	Leaf reflectance in visible range (400-700 nm)	unitless (0-1)	NA	NA
leaf_respiration_rate (Rd0)	Ratio of leaf respiration to Vcmax	???	Leaf respiration*	Leaf Resp*
leaf_trans_nir	Leaf transmittance in NIR range (700-2500 nm)	unitless (0-1)	NA	NA
leaf_trans_vis	Leaf transmittance in visible range (400-700 nm)	unitless (0-1)	NA	NA
leaf_turnover_rate	Temperature dependent rate of leaf loss (conifer only)	year-1	NA	NA
minimum_height	Minimum height for plant reproduction	m	Minimum height	NA
mort1	Time-scale at which low-carbon balance plants die	years-1	Carbon balance mortality	Mortality
mort2	C balance ratio at which mortality rapidly increases	unitless (mass ratio)	NA	NA
mort3	Density-independent (background) mortality rate	year-1	Background mortality	NA
nonlocal_dispersal	Proportion of dispersal that is global	unitless (0-1)	NA	NA
orient_factor	Leaf angle orientation distribution	unitless (-1-1)	NA	NA
quantum_efficiency	Farquhar model parameter (TODO)	mol CO2 (mol photons)-1	Quantum efficiency	Quantum Eff.
r_fract	Fraction of C storage to seed reproduction	unitless	Recruitment carbon	Reproduction?
root_respiration_rate (_factor)	Root respiration rate at 15 °C	μmol CO2 (kg fineroot)-1	Root respiration	NA
root_turnover_rate	Temperature dependent rate of fine root loss	year-1	Root turnover	Root turnover
seedling_mortality	Proportion of seed that dies and goes to litter pool	unitless (0-1)	NA	NA
SLA	Specific leaf area	m2 kg-1 C	Specific leaf area	SLA
stomatal_slope	Slope between A and stomatal conductance (Leuning)	unitless	Stomatal sensitivity	Stomatal Slope
Vcmax (Vm0)	Maximum rate of CO2 carboxylation at 15 °C	μmol m-2 s-1	Vcmax	Vcmax
water_conductance	Water availability factor	m-2 a-1 (kg C root)-1	Soil-plant water conductance	Water Cond

Plant functional types and parameterization

By default, ED-2.2 supports 17 different plant functional types, which divide plant species according to photosynthetic pathway (C3 vs. C4), growth form (grass vs. tree), leaf phenology habit (deciduous vs. evergreen), biome (e.g. temperate vs. tropical), and successional status (e.g. early, mid, late). However, we limited our simulations to the four plant functional types that have any appreciable presence at UMBS: Early, mid, and late temperate deciduous trees and pines. The species comprising these plant functional types are shown in Table 3.

Table 3: Plant functional type-species mappings

Plant functional type	Species	Color
Early hardwood	Betula papyrifera	Violet
	Populus grandidentata
	Populus tremuloides
Mid hardwood	Quercus rubra	Blue
	Acer rubrum
	Acer pensylvaticum
Late hardwood	Acer saccharum	Green
	Fagus grandifolia
Pine	Pinus strobus	Yellow

For each plant functional type, we generated a distribution of parameter values via the Predictive Ecosystem Analyzer (PEcAn) trait-meta analysis (LeBauer et al. 2013, see also Dietze et al. 2014, Raczka et al. 2018). Prior distributions for this meta-analysis were largely adapted from previous ED2 parameter uncertainty studies (Dietze et al. 2014, Raczka et al. 2018, Viskari et al. 2019), and are shown in detail in Supplementary Information X. Species trait data for this meta-analysis came from existing records in the BETY database (www.betydb.org, LeBauer et al. 2017), as well as from publicly available records in the TRY database (www.try-db.org, Kattge et al. 2011) and, specifically for leaf optical properties, from Shiklomanov (2019 {dissertation, chapter 3}). The resulting parameter distributions are shown in Figure 1. All parameters not described in this section were set to their ED-2.2 PFT-specific default values.

Figure 1: Input parameter distributions from PEcAn trait meta-analysis.

Modeling workflow

For each factorial combination of model configurations/submodels (described above), we ran 100 ensemble members from 1901 to 2000. Each ensemble member was initialized from ED2’s “near-bare ground” condition: An equal number of seedlings of each plant functional type (see previous section) at the minimum resolvable size. Driving meteorological data was 6-hourly CRU-NCEP combined with an annual atmospheric CO₂ record from Law-Dome ice core (Etheridge et al. 1998) and Mauna Loa observatory (Thoning et al. 1989). Soil texture was set to 92% sand, 7% silt, and 1% clay, per site-level observations in (Gough et al. 2010). The initial soil moisture profile was set to the average soil moisture profile reported in the UMBS Ameriflux ancillary data (https://ameriflux.lbl.gov/sites/siteinfo/US-UMd). The entire model execution workflow was conducted using the Predictive Ecosystem Analyzer (PEcAn, www.pecanproject.org).

Driver uncertainty is outside the scope of this study, and initial condition uncertainty is minimized by our experimental design, which is conditioned on a specific initial condition (near bare ground).

Analysis of results

• Overall summary:
  • Overall parameter uncertainty – Time-series plots of total annual GPP and NPP, and maximum LAI and AGB, averaged across ensemble members
  • Impact of parameter uncertainty on ecological trajectories – plot of max annual LAI by PFT
  • Both compared against observations of recently observed LAI and NPP at UMBS (e.g. FASET, FoRTE)
• Uncertainty analysis:
  • Parameter vs. structural uncertainty – Variance in mean annual GPP from 19XX to 19YY across ensembles within model structure, and compare against
  • Breakdown of parameter uncertainty – PEcAn sensitivity and uncertainty analysis (LeBauer et al. 2013, Dietze et al. 2014)
• Details of structural uncertainty:
  • Vertical profiles of radiation, traits?

All analyses for this work were performed using R 3.6 (see “Colophon” for full details). Code and supporting data for reproducing this analysis are publicly available on the Open Science Framework (OSF) at https://osf.io/dznuf/.

Results

Summary

Figure 2: ED2 plot-level predictions of gross (GPP) and net (NPP) primary productivity, aboveground biomass (AGB), total leaf area index (LAI), and Shannon diversity index (of plant functional types) by model configuration. The solid line is the ensemble mean. The dashed line is the 80% confidence interval. Black dot with error bars is the mean and min/max value from Hardiman et al. (2013).

Model projections of gross and net primary productivity, aboveground biomass, leaf area index, and functional diversity varied with both parameter value and model structure (Figure 2). One model configuration – finite canopy radius, two-stream radiative transfer, and plastic traits – failed to grow at all, regardless of parameter combinations, and a similar configuration with static traits showed much less growth than any other model configurations. The remaining configurations all exhibited a similar trajectory of rapid growth in the first 15-20 years followed by a gradual decline to a lower, stable value around 1975 (with individual ensemble members sometimes undergoing sudden collapse in specific years). The ensemble mean ecosystem state of most model confugrations had net primary productivity very close to that observed at UMBS, but generally much lower leaf area index. However, the ensemble spread around the mean was large – across all configurations (except the finite canopy - two-stream radiative transfer cases), the spread in net primary productivity was from zero to several times higher than the observed. Ensemble variance in leaf area index was lower on average but, in some case (e.g. finite canopy, multiple-scatter radiative transfer, static traits) was over an order of magnitude. The predicted Shannon diversity index of plant functional types was, on average, higher in simulations when the canopy architecture was finite rather than closed.

Figure 3: Post-1975 growing season averaged NPP vs. LAI, with observation (in black) and linear regression, by model type. Letter labels are selected runs with the same parameters, and match the rows in Figure 4.

Model projections of gross and net primary productivity, aboveground biomass, leaf area index, and functional diversity varied with both parameter value and model structure (Figure 2). The ensemble means of all model configurations exhibited a similar trajectory of rapid growth in the first 15-20 years followed by a gradual decline throughout the rest of the simulation (with individual ensemble members sometimes undergoing sudden collapse in specific years). However, the average rate of decline varied by model configuration, particularly the crown model: Compared to models with a “closed” canopy (i.e. complete shading; no horizontal competition), models with a “finite” canopy predicted slightly faster decline in net primary productivity and functional diversity. This decline was most severe in configurations that combined the finite canopy and two-stream radiative transfer; in these configurations, a disproportionately large number of ensembles experienced complete ecosystem collapse over the course of the simulation, and the overwhelming fraction of ensemble members predicted near-zero Shannon diversity after 30 years. Besides this specific configuration, which consistently under-predicted observed net primary productivity at UMBS, the remaining model configurations had ensemble mean net primary productivity values that were very close to the mean observed value from Hardiman et al. (2013). Moreover, the ensemble spread of net primary productivity from these configurations was very similar to the uncertainty in the observations, though the distribution was relatively balanced for model predictions but skewed positive for the observations.

Patterns in leaf area index were somewhat distinct from patterns in productivity and diversity. While model configurations with finite canopy and two-stream radiative transfer again predicted the lowest leaf area index on average, model configurations with finite canopy and multiple-scatter predicted the highest leaf area index on average. The latter configurations also had the largest number of ensemble members that fell within the observed distribution of leaf area index; meanwhile, every model configuration predicted an ensemble mean leaf area index at the end of the simulation that was significantly below the observation from Hardiman et al. (2013).

Figure 4: PFT-level predictions of leaf area index (LAI) by model configuration and parameterization. Each row of plots is a simulation with the same set of parameters across model configurations. Letters correspond to the labels in Figure 3. Note that these are predictions of total leaf area index summed across all cohorts of the same PFT, meaning that higher LAI in one PFT does not necessarily indicate dominance, size, etc.

Different parameter combinations led to model outputs that had not only different bulk ecosystem properties but also qualitatively different plant communities (Figure 3). The most common outcome was immediate and persistent dominance by early hardwood trees, though in some cases, early hardwoods co-existed with late hardwood or pine.

Figure 4: Time-averaged NPP vs. LAI, with observation (in black) and linear regression, by model type.

Uncertainty analysis

Figure 5: Comparison of parameteric uncertainty within ensembles (colored bars, colored by model type) and “structural” uncertainty (variance in ensemble means; black bar) by output variable. Output variables are expressed as growing season averages for all years after 1910.

Except for the configurations with persistently low productivity, parameter uncertainty (across ensembles within each model configuration) was much larger than structural uncertainty (variance in ensemble means across configurations; Figure 4). The relative importance of parameter uncertainty varied with both model configuration and the variable in question. Allowing SLA and V_cmax to vary with light level (warm colors, as opposed to static traits – cool colors) slightly reduced variability in primary productivity, slightly increased variability in Shannon diversity, and had mixed effects on aboveground biomass and total leaf area. Enabling the finite canopy radius (dark colors; compared to closed canopy – light colors) dramatically decreased variability in primary productivity and Shannon diversity and increased variability in leaf area, and had mixed effects on aboveground biomass. reduced variance in aboveground biomass, diversity, and primary productivity. Finally, using a multiple-scatter (secondary colors) rather than a two-stream (primary colors) radiative transfer scheme increased variance in leaf area index, aboveground biomass, and diversity, but did not have a consistent effect on variance in productivity productivity.

Figure 6: PEcAn-like parameter sensitivity and uncertainty analysis, by model type. Elasticity (a) is the normalized sensitivity of the model to a fixed change in the parameter. pvar (b) is the partial variance, which describes the overall contribution of the parameter to model predictive uncertainty based on the combination of parameter uncertainty and model sensitivity. Input parameter distributions are shown in Figure 1.

Model sensitivity to specific parameters (“elasticity” sensu …) varied depending on the model configuration and the target output variable (Figure 5). For predicting C fluxes, biomass, and leaf area, the three most important parameters in terms of model sensitivity were specific leaf area (SLA) for early and late hardwoods, leaf C:N ratio (c2n_leaf) for early and mid hardwoods, and V_cmax for mid and late hardwoods. Both the magnitude and direction of sensitivity to these parameters varied by model configuration. For example, in the default ED2 configuration (closed canopy, two-stream radiative transfer, static traits), net primary productivity increased with early hardwood specific leaf area, but when this configuration was altered so SLA and V_cmax could vary with light level, net primary productivity decreased with early hardwood specific leaf area. Similarly, the model became much more sensitive to early- and mid-hardwood leaf C:N ratio when switching from a closed canopy to a finite canopy configuration.

The parameters that contributed most to overall model predictive uncertainty (“partial variance”) differed the parameters to which the model was most sensitive (Figure 5), largely driven by the fact that many of the parameters with the highest sensitivity (e.g. SLA, V_cmax) were also well constrained by data (Figure 1). Patterns in partial variance were largely idiosyncratic across model configurations; when we considered the top-5 most important parameters for a given output variable and model configuration, only five combinations were present in at least half of the model configurations: growth respiration, C balance mortality ratio (mort2), and stomatal slope (all for early hardwoods).

Discussion

• Parameter uncertainty is the dominant driver of model predictive uncertainty.

• …but the nature of this parameter uncertainty depends on model configuration.

• Ecological implications of structural uncertainty

  • Predictions about ecological succession are very sensitive to the understory light environment.
    • Need a good representation of canopy structure (finite canopy radius)
    • How you model canopy radiative transfer matters! Small differences in the model can give significant results.
  • But, trait plasticity can provide an alternative mechanism for success in the understory.
    • Important modeling implication for all the emerging research on intra-specific trait variability.
    • This combination of discrete functional types with plastic traits is closer to reality than purely trait-based (“eco-evolutionary?”) models or completely discretized models with static traits on the other.
    • Important caveat: Current implementation is based entirely on tropical data, which has more extreme canopy shading than temperate forests (REF), so tropical species may have evolved stronger trait plasticity than temperate species (REF).
    • Perhaps note “ecological equifinality” here: there are different ways to arrive at similar outcomes in the model; this is also true in nature?

• Implications of uncertainty analysis for future data collection and model development

  • Parameter uncertainty is still a huge source of overall model predictive uncertainty. Different parameters can give qualitatively different ecological outcomes.
  • Looking beyond aggregate variables (e.g. net primary productivity, total LAI) is essential to model evaluation and calibration. It’s possible to generate a relatively?
  • (Expected) Subsurface parameters (e.g. leaf-root ratios) have high sensitivity, but are poorly constrained.
  • Trait covariance may alleviate some data limitation (Shiklomanov et al. 2018 [preprint])

• Comparisons against other studies

  • Parameter sensitivity
    • (Pandit et al. 2018) – Most important parameters for shrubs were SLA, Vcmax, stomatal slope, root:leaf ratio, and root turonver rate (slightly less important: leaf turnover rate, growth respiration, cuticular conductance; much less important: water conductance; basically irrelevant: storage turnover, leaf width)
    • Compare against Dietze et al. (2014) and Raczka et al. (2018)

• Future directions: Predicting disturbance response

  • FoRTE project – Forecasting a disturbance.
    • Compare ecological resilience/memory between model and reality

Moreover, these models’ predictions of species composition and ecosystem structure are relevant outside of carbon cycle science, particularly for forest management and wildlife conservation.

Conclusions

Acknowledgements

This project funded by NSF grant. Cyberinfrastructure provided by Pacific Northwest National Laboratory (PNNL). Data from University of Michigan Biological Station (UMBS). Data from TRY (TODO: Specific TRY statement).

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Appendix 1: Submodel descriptions

Radiative transfer: Definitions

• \(\omega\) – Clumping factor
• \(LAI\) – Leaf area index
• \(TAI\) – Total area index (leaf and woody area)
• \(LAI_e\) / \(TAI_e\) – “Effective” area indices (accounting for clumping)

Two-stream RTM

Multiple scatter RTM

Effective LAI is just true LAI x clumping.

\[ LAI_e = \omega LAI \]

Total area index (TAI) is leaf (LAI) + wood (WAI) area.

\[ TAI_e = LAI_e + WAI \]

Local exposed total area index (\(TAI_l\)) is the total area index divided by crown area index (\(CAI\)).

\[ TAI_{l} = \frac{TAI_e}{CAI} \]

Leaf (\(w_l\)) and wood (\(w_w\)) weights:

\[ w_l = \frac{LAI_e}{TAI_e} \] \[ w_w = 1 - w_l \]

Projected area (\(a_{proj}\)), based on coefficients \(\phi_1\) and \(\phi_2\).

\[ a_{proj} = \phi_1 + \phi_2 \mu \]

Optical depth (\(\lambda\)) is projected area over optical depth (\(\mu\))

\[ \lambda = \frac{a_{proj}}{\mu} \]

Transmittance for direct radiation of a canopy layer (\(\tau_{beam}\)) is:

\[ \tau_{beam} = (1 - CAI) + CAI exp\left( -\lambda TAI_l \right) \]

Transmittance for diffuse radiation of a canopy layer (\(\tau_{diff}\)):

\[ ext_1 = \phi_1 TAI_l \] \[ ext_2 = \phi_2 TAI_l \] \[ \tau_{diff} = (1 - CAI) - CAI exp\left( -ext_1 - ext_2 \right) ext_1^2 e^{exp_1} E_i(-exp_1) + (ext_1 - 1)\]

where \(E_i\) is the exponential integral.

Single-scattering albedo (\(w_0\)):

\[ w_0 = \frac{1}{2} \frac{a_{proj}}{\phi_2 \mu + a_{proj}} \frac{1 - \phi_1 \mu}{\phi_2 \mu a_{proj}} \log \left( 1 + \frac{\phi_2 \mu + a_{proj}}{\phi_1 \mu} \right) \]

Beam backscatter (\(\gamma\)):

\[ \gamma = w_0 \frac{1 + \bar{\mu} \lambda}{\bar{\mu} \lambda} \]

Old outline

Introduction

• Why we need models?
  • Forests are important, for C sequestration, other ecosystem services
  • Policy decisions related to forests depend on future projections
  • We need models to make future projections
• What kinds of models are out there?
  • Traditional: “Big leaf” models
    • Needed to be simple to run on old computers
    • Don’t need as much data
    • …but they fail to capture important processes, which matter not only for accurate predictions about C cycle, but also because they are processes we care about (habitat, forestry, tourism, etc.)!
  • Individual-based models
    • Much more detailed, but harder to run, and need much more data.
    • Trade-off between complexity and accuracy.
• Cohort-based models like ED2 as a middle ground?
  • Core ED concept (Moorcroft et al. 2001)
  • ED2 developments – (Medvigy et al. 2009, Medvigy and Moorcroft 2011)
  • Most recent version – (Longo et al. 2019b)
  • Validation/applications of the ED model:
    • (Rollinson et al. 2017) – ED2 paleoclimate
    • (Miller et al. 2015) – ED2 at Duke FACE
    • (De Kauwe et al. 2013) – ED2 at Duke and Oak Ridge FACE
    • (Longo et al. 2019a) – Model evaluation in Tropics
• How much complexity do we need to accurately model ecological dynamics?
  • Lots of existing work on parametric uncertainty
    • (Dietze et al. 2014)
    • (Raczka et al. 2018)
    • (Pandit et al. 2018)
  • Less on structural uncertainty – i.e. not just what coefficients do we use, but what equations, and more generally, what processes do we even consider?
• What are the processes that drive succession of ecological communities?
  • Competition for light (Bazzaz 1979)
  • Others? Leaning towards omitting because factorial combination becomes too large.
    • Competition for water?
    • Competition for nutrients? (ED’s N model isn’t very good. Alternatives are being developed, but not in ED mainline yet.)
• Brief review of community/ecosystem ecology of the Upper Midwest
  • UMBS is a useful site for testing these theories because of its natural history.
  • Around 1900, mature forest dominated by white (Pinus strobus) and red pine (Pinus resinosa), hemlock (Tsuga canadensis), and sugar maple (Acer saccharum).
  • But, repeat harvest and burning between 1880 and 1920 (Kilburn 1960) led to replacement by early successional aspen (Populus grandidentata and Populus tremuloides), birch (Betula papyrifera), and cherry (Prunus pensylvatica) (???, Gates 1930, Friedman and Reich 2005, Bergen and Dronova 2007).
  • Such aspen-dominated secondary forests are sustained by background levels of disturbance, particularly fire (Gates 1930)
  • However, due to aggressive fire suppression in the US, these forests are now undergoing succession, primarily to mid/late-successional hardwood (typified by sugar maple and American beech, Fagus grandifolia) or upland conifer (typified by red and white pine) (Bergen and Dronova 2007).
  • The combination of stand-replacing disturbance ~100 years ago and suppressed disturbance since then makes this an ideal site for testing a vegetation model run from bare ground without having to prescribe disturbance.
• Guiding questions:
  • Which of these processes do we need to be able to accurately model what happens (“community succession and C cycle dynamics”) to Midwestern forests?
  • What is the cost of considering these processes, in terms of additional parametric uncertainty?
  • What are the relative contributions of parametric uncertainty (data limitation) vs. structural uncertainty (theoretical limitation?)?
• Study overview:
  • ED with factorial combination of submodels related to radiative transfer formulation (two-stream vs. multiple scatter), horizontal competition (finite canopy radius vs. complete shading), and trait plasticity (whether or not SLA and Vcmax vary with light level)
  • Ensemble analysis to look at parameter uncertainty

\[ \lambda = \frac{a_{proj}}{\mu} \]

Methods

Site description

• Secondary successional forest – bigtooth aspen (Populus grandidentata), northern red oak (Quercus rubra), red maple (Acer rubrum), paper birch (Betula papyrifera), eastern white pine (Pinus strobus)
• Average age – 95 years (2013)
• NEP in UMBS tower is 1.58 MG C ha^-1 yr^-1 (0.80-1.98) (1999-2006), but with landscape variation (REF?)
• Heavily logged in late 1800s and early 1900s, disturbed by fire until 1923 (REF)
• Present day composition typical of upper Great Lakes region
• Previously, the site of the FASET experiment (Gough et al. 2008, 2013)
• UMBS is 87% upland and 13% wetland (Bergen and Dronova 2007). We focus on the upland ecosystem, which has the following characteristics (from Bergen and Dronova (2007)):
  • 20.4% moraine, 37.8% high outwash plain, 31.3% low outwash plain, 5.7% lake-margin terrace, 3.6% ice-contact, 1.2% lowland glacial lake
  • 60.9% aspen-dominated, 16.6% northern hardwood (Acer saccharum, Acer rubrum, Fagus grandifolia, Tilia americana (basswood), Betula alleghaniensis (yellow birch), Fraxinus americana (white ash), Tsuga canadensis), 13.3% upland conifer (Pinus strobus, Pinus resinosa)
  • 1.6% northern red oak (Quercus rubra)
  • 60.9% transitioning from aspen to next succession, of which: 55.8% to northern hardwood, 34.7% to upland conifer, 3.8% to northern red oak, 2.6% to northern red oak-red maple, 3.1% to upland conifer-northern hardwood

PFT definitions

• Early successional hardwood
  • Betula papyrifera (white/paper birch)
  • Populus grandidentata (bigtooth aspen)
  • Populus tremuloides (trembling aspen)
• Mid successional hardwood
  • Quercus rubra (red oak)
  • Acer rubrum (red maple)
  • Acer pensylvaticum (striped maple)
• Late successional hardwood
  • Acer saccharum (sugar maple)
  • Fagus grandifolia (American beech)
• Pine
  • Pinus strobus (white pine)
• Omitted candidates
  • Early hardwood
    • Prunus pensylvatica (fire cherry)
  • Mid hardwood
    • Betula alleghaniensis (yellow birch)
    • Tilia americana (basswood)
    • Fraxinus americana (white ash)
  • Late hardwood
    • Ostyra virginiana (hop-hornbeam)
  • Pine
    • Pinus resinosa (red pine)

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Colophon

This report was generated on 2019-07-11 16:10:12 using the following computational environment and dependencies:

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The current Git commit details are:

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#> Head:     [3ae6c8e] 2019-07-11: Fix capitalization and punctuation in colophon

View this project on GitHub in repository ashiklom/fortebaseline (this manuscript file is in analysis/paper/paper.Rmd) and in Open Science Framework (OSF) at https://osf.io/dznuf/ .